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For reactions where we see multiple reactants, we design an experiment such that all the reagents' concentrations are constant so that we can change one significantly(which would be at a low concentration) and see how it changes the rate law. Thus by doing this for reactant we can determine the order of each reactant, the order of the reaction and the rate law.
When determining the rate laws of a reaction with multiple reactants, we use the reactant of the smallest concentration because that reactant will determine the rate of the overall reactions. Since the other reactants are in excess, they don't really affect the rate of the reaction. This way, we are able to see how each reactant affects the rate of the reaction so we can figure out the order of each reactant.
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